Solving fermion problems without solving the sign problem: Symmetry-breaking wave functions from...

Area of Science:

• Computational Physics
• Quantum Many-Body Systems
• Quantum Dots

Background:

• The primitive second-order propagator in path-integral Monte Carlo (PIMC) calculations for many-fermion systems is known to cause the sign problem.
• This sign problem significantly hinders accurate simulations of complex quantum systems, including quantum dots.

Purpose of the Study:

• To demonstrate a method that overcomes the sign problem in PIMC calculations for many-fermion systems.
• To accurately determine the ground state of large quantum dots with a significant number of electrons.

Main Methods:

• Utilized a similarity-transformed Fokker-Planck propagator instead of the traditional second-order propagator.
• Applied the method to calculate the ground state of quantum dots containing up to 100 polarized electrons.

Main Results:

• Successfully solved for the ground state of large quantum dots without encountering the sign problem.
• The similarity-transformed propagators naturally yield rotational symmetry-breaking ground-state wave functions.
• Identified that optimal electron localization occurs at positions maximizing the bosonic ground-state wave function, not minimizing potential energy.

Conclusions:

• The similarity-transformed Fokker-Planck propagator offers a viable solution to the sign problem in PIMC simulations of many-fermion systems.
• This approach facilitates the study of large quantum dots and related phenomena like the quantum Hall effect.
• Employing these wave functions as initial states in subsequent PIMC calculations can further enhance energy accuracy.